We study the phases of a Schwarzschild black hole in the Anti-deSitter background geometry. Exploiting fluid/gravity duality, we construct the Maxwell equal area isotherm&#x2009;&#x2009;<svg     style="vertical-align:-0.0pt;width:49.799999px;" id="M1" height="13.75" version="1.1" viewBox="0 0 49.799999 13.75" width="49.799999"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,13.688)"><path id="x1D447" d="M649 676l-22 -187l-33 -2q3 56 -12 94q-8 20 -31.5 26.5t-86.5 6.5h-74l-90 -491q-4 -23 -6 -36.5t1 -25t7 -16.5t18 -9t27 -5t41 -3l-6 -28h-286l4 28q68 5 84 18.5t28 76.5l94 491h-55q-74 0 -100.5 -6t-41.5 -23q-24 -29 -54 -98l-32 1q32 98 53 188h22q7 -18 15 -22&#xA;t37 -4h417q23 0 33.5 5t25.5 21h23z" /></g><g transform="matrix(.017,-0,0,-.017,16.092,13.688)"><path id="x3D" d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" /></g><g transform="matrix(.017,-0,0,-.017,30.796,13.688)"><use xlink:href="#x1D447"/></g>

			<g transform="matrix(.012,-0,0,-.012,42.125,5.525)"><path id="x2217" d="M471 153q-22 -15 -61 -13q-25 31 -45.5 49.5t-56.5 41.5q4 -71 28 -134q-17 -33 -42 -46q-24 12 -42 46q24 63 28 134q-36 -23 -56.5 -41.5t-45.5 -49.5q-36 -2 -61 13q0 28 19 59q65 10 130 43q-65 33 -130 43q-19 31 -19 59q22 15 61 13q25 -31 45.5 -49.5t56.5 -41.5&#xA;q-4 71 -28 134q17 33 42 46q24 -12 42 -46q-24 -63 -28 -134q36 23 56.5 41.5t45.5 49.5q36 2 61 -13q0 -28 -19 -59q-65 -10 -130 -43q65 -33 130 -43q19 -31 19 -59z" /></g>

		
	
</svg> in the temperature-entropy plane, in order to eliminate negative heat capacity BHs. The construction we present here is reminiscent of the isobar cut in the pressure-volume plane which eliminates unphysical part of the Van der Walls curves below the critical temperature. Our construction also modifies the Hawking-Page phase transition. Stable BHs are formed at the temperature <svg     style="vertical-align:-0.04095pt;width:49.799999px;" id="M2" height="13.8" version="1.1" viewBox="0 0 49.799999 13.8" width="49.799999"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,13.688)"><use xlink:href="#x1D447"/></g><g transform="matrix(.017,-0,0,-.017,16.092,13.688)"><path id="x3E" d="M512 230l-437 -233v58l378 199v2l-378 200v58l437 -233v-51z" /></g><g transform="matrix(.017,-0,0,-.017,30.796,13.688)"><use xlink:href="#x1D447"/></g>

			<g transform="matrix(.012,-0,0,-.012,42.125,5.525)"><use xlink:href="#x2217"/></g>

		
	
</svg>, while pure radiation persists for <svg     style="vertical-align:-0.04095pt;width:49.799999px;" id="M3" height="13.8" version="1.1" viewBox="0 0 49.799999 13.8" width="49.799999"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,13.688)"><use xlink:href="#x1D447"/></g><g transform="matrix(.017,-0,0,-.017,16.092,13.688)"><path id="x3C" d="M512 -3l-437 233v51l437 233v-58l-378 -200v-2l378 -199v-58z" /></g><g transform="matrix(.017,-0,0,-.017,30.796,13.688)"><use xlink:href="#x1D447"/></g>

			<g transform="matrix(.012,-0,0,-.012,42.125,5.525)"><use xlink:href="#x2217"/></g>

		
	
</svg>. <svg     style="vertical-align:-0.0pt;width:19.049999px;" id="M4" height="13.75" version="1.1" viewBox="0 0 19.049999 13.75" width="19.049999"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,13.688)"><use xlink:href="#x1D447"/></g>

			<g transform="matrix(.012,-0,0,-.012,11.388,5.525)"><use xlink:href="#x2217"/></g>

		
	
</svg> turns out to be below the standard Hawking-Page temperature and there are no unstable BHs as in the usual scenario. Also, we show that, in order to reproduce the correct BH entropy <svg     style="vertical-align:-2.22495pt;width:55.325001px;" id="M5" height="14.85" version="1.1" viewBox="0 0 55.325001 14.85" width="55.325001"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,12.012)"><path id="x1D446" d="M457 488l-30 -3q-17 148 -131 148q-53 0 -84.5 -34.5t-31.5 -82.5q0 -42 25.5 -72t74.5 -62l33 -22q63 -42 95 -85t32 -102q0 -84 -67 -137t-163 -53q-58 0 -113 22t-70 43l-4 152l27 4q4 -32 15 -62.5t31 -59.5t53.5 -47t76.5 -18q56 0 92 35t36 96q0 39 -25 70t-78 68&#xA;l-31 22q-32 23 -53.5 41.5t-45 57t-23.5 77.5q0 82 58 132.5t156 50.5q46 0 101 -17l18.5 -6t17 -6t8.5 -3q-4 -55 0 -147z" /></g><g transform="matrix(.017,-0,0,-.017,12.931,12.012)"><use xlink:href="#x3D"/></g><g transform="matrix(.017,-0,0,-.017,27.634,12.012)"><path id="x1D434" d="M716 28l-8 -28h-254l8 28q55 5 66 17.5t5 47.5l-30 145h-232l-74 -138q-21 -43 -11 -54.5t72 -17.5l-6 -28h-235l8 28q53 7 73.5 21t53.5 70l319 540l33 8q6 -43 33 -176l80 -381q10 -49 26.5 -63t72.5 -19zM495 281l-49 264h-2l-149 -264h200z" /></g><g transform="matrix(.017,-0,0,-.017,40.095,12.012)"><path id="x2F" d="M368 703l-264 -866h-60l265 866h59z" /></g><g transform="matrix(.017,-0,0,-.017,47.098,12.012)"><path id="x34" d="M456 178h-96v-72q0 -51 12.5 -62.5t72.5 -16.5v-27h-256v27q65 5 78 17t13 62v72h-260v28q182 271 300 426h40v-407h96v-47zM280 225v295h-2q-107 -148 -196 -295h198z" /></g>

		
	
</svg>, one has to write a black hole equation of state, that is, <svg     style="vertical-align:-2.3205pt;width:65.550003px;" id="M6" height="15.0875" version="1.1" viewBox="0 0 65.550003 15.0875" width="65.550003"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,12.138)"><path id="x1D443" d="M619 482q0 -69 -40.5 -119t-96 -72.5t-118.5 -26.5h-44l-70 20l-31 -151q-14 -67 0.5 -83t89.5 -22l-5 -28h-287l8 28q65 7 81.5 22t29.5 83l79 398q12 56 0.5 70.5t-78.5 20.5l7 28h255q108 0 164 -43t56 -125zM524 478q0 141 -146 141q-25 0 -47 -8q-16 -6 -20.5 -13.5&#xA;t-10.5 -39.5l-43 -241q37 -13 83 -13q67 0 125.5 45t58.5 129z" /></g><g transform="matrix(.017,-0,0,-.017,15.582,12.138)"><use xlink:href="#x3D"/></g><g transform="matrix(.017,-0,0,-.017,30.286,12.138)"><use xlink:href="#x1D443"/></g><g transform="matrix(.017,-0,0,-.017,41.097,12.138)"><path id="x28" d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" /></g><g transform="matrix(.017,-0,0,-.017,46.979,12.138)"><path id="x1D449" d="M730 650l-8 -28q-52 -4 -72 -18t-64 -77q-79 -113 -321 -539h-33l-119 541q-13 59 -29.5 73t-66.5 20l7 28h245l-8 -28l-28 -5q-33 -6 -40.5 -15.5t-0.5 -38.5l102 -450h2q191 320 246 430q21 42 15.5 56t-43.5 19l-31 4l7 28h240z" /></g><g transform="matrix(.017,-0,0,-.017,59.592,12.138)"><path id="x29" d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" /></g>

		
	
</svg>, in terms of the geometrical volume <svg     style="vertical-align:-3.276pt;width:83.762497px;" id="M7" height="19.924999" version="1.1" viewBox="0 0 83.762497 19.924999" width="83.762497"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,15.775)"><use xlink:href="#x1D449"/></g><g transform="matrix(.017,-0,0,-.017,17.384,15.775)"><use xlink:href="#x3D"/></g><g transform="matrix(.017,-0,0,-.017,32.088,15.775)"><use xlink:href="#x34"/></g><g transform="matrix(.017,-0,0,-.017,40.248,15.775)"><path id="x1D70B" d="M574 449q-23 -58 -38 -79q-16 -4 -79 -4q-27 -100 -46 -219q-14 -87 7 -87t74 36l13 -27q-74 -81 -139 -81q-48 0 -48 62q0 22 8 59l60 258l-154 4q-21 -103 -54.5 -209t-64.5 -151q-38 -23 -83 -23l-7 15q46 36 94 152.5t64 216.5q-81 0 -138 -54l-18 23q22 27 39.5 43&#xA;t61.5 33.5t100 17.5q43 0 131.5 -2.5t129.5 -2.5q23 0 33.5 5t24.5 25z" /></g><g transform="matrix(.017,-0,0,-.017,50.294,15.775)"><path id="x1D45F" d="M393 379q-9 -16 -28 -29q-15 -10 -23 -2q-19 19 -36 19q-21 0 -52 -38q-57 -72 -82 -126l-40 -197q-23 -3 -75 -18l-7 7q49 196 74 335q7 43 -2 43q-7 0 -30 -14.5t-47 -37.5l-16 23q37 42 82 73t67 31q41 0 15 -113l-11 -50h4q41 71 85 117t77 46q29 0 45 -26&#xA;q13 -21 0 -43z" /></g>

			<g transform="matrix(.012,-0,0,-.012,57.475,7.613)"><path id="x33" d="M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5&#xA;q0 45 -26.5 69.5t-68.5 24.5q-67 0 -120 -79l-20 20l43 63q51 56 127 56h1q66 0 107 -37t41 -95q0 -42 -31 -71q-22 -23 -68 -54z" /></g><g transform="matrix(.012,-0,0,-.012,57.475,19.863)"><path id="x1D43B" d="M865 650q-1 -4 -4 -14t-4 -14q-62 -5 -77 -19.5t-29 -82.5l-74 -394q-12 -61 -0.5 -77t75.5 -21l-6 -28h-273l8 28q64 5 82 21t29 76l36 198h-380l-37 -197q-11 -64 0.5 -78.5t79.5 -19.5l-6 -28h-268l6 28q60 6 75.5 21.5t26.5 76.5l75 394q13 66 2 81.5t-77 20.5l8 28&#xA;h263l-6 -28q-58 -5 -75.5 -21t-30.5 -81l-26 -153h377l29 153q12 67 2 81t-74 21l5 28h268z" /></g>

			<g transform="matrix(.017,-0,0,-.017,68.538,15.775)"><use xlink:href="#x2F"/></g><g transform="matrix(.017,-0,0,-.017,75.541,15.775)"><use xlink:href="#x33"/></g>

		
	
</svg>.

Euro Spallucci

Anais Smailagic

Maxwell&#x2019;s Equal Area Law and the Hawking-Page Phase Transition

The difference between Einstein's general relativity and its Cartan extension is analyzed within
the scenario of <i>asymptotic safety</i> of quantum gravity. In particular, we focus on the four-fermion
interaction which distinguishes the Einstein-Cartan theory from its Riemannian limit.

Eckehard W. Mielke

Is Einstein-Cartan Theory Coupled to Light Fermions Asymptotically Safe?

We resolve here an outstanding problem plaguing conformal gravity in its
role in making consistent astrophysical predictions. Though its static
spherically symmetric solution incorporates all the successes of
Schwarzschild gravity, the fit to observed galactic rotation curves requires
<svg style="vertical-align:-3.56265pt;width:36.224998px;" id="M1" height="15.35" version="1.1" viewBox="0 0 36.224998 15.35" width="36.224998" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,10.862)"><path id="x1D6FE" d="M478 372q0 -39 -31 -97t-61 -98t-78 -98q-45 -55 -73 -102q-13 -79 -13 -197q-11 -11 -43.5 -25.5t-53.5 -15.5l-15 17q5 35 26 101.5t47 123.5q8 72 -1.5 174.5t-37.5 178.5q-14 37 -29 37q-20 0 -67 -65l-25 21q37 60 73 90.5t63 30.5q47 0 72 -112q13 -56 17.5 -141.5&#xA;t0.5 -143.5h2q155 193 155 297q0 26 -12 47q-5 8 -5 15q0 16 12.5 27t29.5 11q21 0 34 -21t13 -55z" /></g><g transform="matrix(.017,-0,0,-.017,13.288,10.862)"><path id="x3E" d="M512 230l-437 -233v58l378 199v2l-378 200v58l437 -233v-51z" /></g><g transform="matrix(.017,-0,0,-.017,27.991,10.862)"><path id="x30" d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105&#xA;q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" /></g></svg>, while the observed increase in the Schwarzschild light
deflection by galaxies appears to demand <svg style="vertical-align:-3.56265pt;width:36.224998px;" id="M2" height="15.35" version="1.1" viewBox="0 0 36.224998 15.35" width="36.224998" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,10.862)"><use xlink:href="#x1D6FE" /></g><g transform="matrix(.017,-0,0,-.017,13.288,10.862)"><path id="x3C" d="M512 -3l-437 233v51l437 233v-58l-378 -200v-2l378 -199v-58z" /></g><g transform="matrix(.017,-0,0,-.017,27.991,10.862)"><use xlink:href="#x30" /></g></svg>. Here we show that,
contrary to common knowledge, there is an <i>increase</i> in the
Schwarzschild deflection angle in the vicinity of galaxies due purely to the
effect of <svg style="vertical-align:-3.56265pt;width:36.224998px;" id="M3" height="15.35" version="1.1" viewBox="0 0 36.224998 15.35" width="36.224998" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,10.862)"><use xlink:href="#x1D6FE" /></g><g transform="matrix(.017,-0,0,-.017,13.288,10.862)"><use xlink:href="#x3E" /></g><g transform="matrix(.017,-0,0,-.017,27.991,10.862)"><use xlink:href="#x30" /></g></svg>, when the idea of the Einstein-Strauss vacuole model
is employed. With the inconsistency now out of the way, conformal gravity should be
regarded as a good theory explaining light deflection by galaxies.

Debasish Saha

Amarjit Tamang

Ramil Izmailov

Carlo Cattani

Kamal K. Nandi

First-Order Light Deflection by Einstein-Strauss Vacuole Method

Spin foam models, loop quantum gravity, and group field theory are discussed as quantum gravity candidate theories and usually involve a continuous Lie group. We advocate here to consider quantum gravity-inspired models with finite groups, firstly as a test bed for the full theory and secondly as a class of new lattice theories possibly featuring an analogue diffeomorphism symmetry. To make these notes accessible to readers outside the quantum gravity community, we provide an introduction to some essential concepts in the loop quantum gravity, spin foam, and group field theory approach and point out the many connections to the lattice field theory and the condensed-matter systems.

Benjamin Bahr

Bianca Dittrich

James P. Ryan

Spin Foam Models with Finite Groups

It is shown how Einstein's equation can account for the evolution of the universe without an initial singularity and can explain the inflation epoch as a momentum dominated era in which energy from matter and radiation drove extremely accelerated expansion of space. It is shown how an object with momentum loses energy to the expanding universe and how this energy can contribute to accelerated spatial expansion more effectively than vacuum energy, because virtual particles, the source of vacuum energy, can have negative energy, which can cancel any positive energy from the vacuum. Radiation and matter with momentum have positive but decreasing energy in the expanding universe, and the energy lost by them can contribute to accelerated spatial expansion between galactic clusters, making dark energy a classical effect that can be explained by general relativity without quantum mechanics, and, as (13) and (15) show, without an initial singularity or a big bang. This role of momentum, which was overlooked in the Standard Cosmological Model, is the basis of a simpler model which agrees with what is correct in the old model and corrects what is wrong with it.

Kenneth J. Epstein

Nonsingular Einsteinian Cosmology: How Galactic Momentum Prevents Cosmic Singularities

Pierre-Henri Chavanis

A Cosmological Model Based on a Quadratic Equation of State Unifying Vacuum Energy, Radiation, and Dark Energy

The present research paper derives a formula for gravitational force acting between the black hole and light particle passing near the radius of event horizon of black holes and calculates also their values of different test black holes existing in only X-ray binaries (XRBs).

Dipo Mahto

Md Shams Nadeem

Mahendra Ram

Kumari Vineeta

Gravitational Force between the Black Hole and Light Particle in XRBs

We use the theory of teleparallelism equivalent to general relativity based on noncommutative spacetime coordinates. In this context, we write the corrections of the Schwarzschild solution. We propose the existence of a Weitzenb&#xf6;ck spacetime that matches the corrected metric tensor. As an important result, we find the corrections of the gravitational energy in the realm of teleparallel gravity due to the noncommutativity of spacetime. Then we interpret such corrections as a manifestation of quantum theory in gravitational field.

S. C. Ulhoa

R. G. G. Amorim

On Noncommutative Corrections of Gravitational Energy in Teleparallel Gravity

We study how may vary the gravitational and the cosmological &#x201c;constants,&#x201d; (<svg     style="vertical-align:-0.23206pt;width:12.4375px;" id="M1" height="11.75" version="1.1" viewBox="0 0 12.4375 11.75" width="12.4375"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,11.4)"><path id="x1D43A" d="M713 296l-5 -25q-47 -7 -59 -20t-23 -72l-15 -79q-9 -48 -3 -74q-15 -3 -55 -13t-63 -15t-59.5 -10t-70.5 -5q-149 0 -243 80t-94 220q0 169 127.5 276.5t336.5 107.5q91 0 206 -36l-10 -165l-29 -1q1 85 -47.5 126t-146.5 41q-153 0 -243.5 -97t-90.5 -242&#xA;q0 -122 68.5 -198.5t188.5 -76.5q121 0 139 75l20 86q13 58 -1.5 70.5t-99.5 20.5l5 26h267z" /></g>

		
	
</svg> and <svg     style="vertical-align:-0.0pt;width:11.7875px;" id="M2" height="11.425" version="1.1" viewBox="0 0 11.7875 11.425" width="11.7875"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,11.363)"><path id="x39B" d="M671 0h-247v28q49 7 60 18.5t0 45.5l-155 438h-2q-21 -61 -74 -204.5t-75 -210.5q-15 -51 -4.5 -65t67.5 -22v-28h-221v28q50 9 69 26.5t45 84.5l202 517l32 9l194 -535q23 -61 42 -78.5t67 -23.5v-28z" /></g>

		
	
</svg>) in several scalar-tensor theories with Bianchi III, <svg     style="vertical-align:-3.3907pt;width:24.200001px;" id="M3" height="15.4" version="1.1" viewBox="0 0 24.200001 15.4" width="24.200001"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><path id="x56" d="M687 650v-28q-52 -6 -71.5 -23t-47.5 -83q-142 -346 -208 -527h-31q-119 325 -207 545q-21 54 -39.5 68.5t-65.5 19.5v28h245v-28q-52 -5 -61.5 -15.5t3.5 -43.5q55 -157 166 -437h2q120 303 158 421q14 43 3.5 55.5t-71.5 19.5v28h225z" /></g><g transform="matrix(.017,-0,0,-.017,12.013,11.112)"><path id="x49" d="M303 0h-265v28q62 5 76 19.5t14 77.5v400q0 63 -14 77.5t-76 19.5v28h265v-28q-62 -5 -76 -19.5t-14 -77.5v-400q0 -64 14 -78t76 -19v-28z" /></g>

			<g transform="matrix(.012,-0,0,-.012,17.812,15.187)"><path id="x30" d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105&#xA;q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" /></g>

		
	
</svg>, and <svg     style="vertical-align:-3.3907pt;width:24.637501px;" id="M4" height="15.4" version="1.1" viewBox="0 0 24.637501 15.4" width="24.637501"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,11.112)"><use xlink:href="#x56"/></g><g transform="matrix(.017,-0,0,-.017,12.013,11.112)"><use xlink:href="#x49"/></g>

			<g transform="matrix(.012,-0,0,-.012,17.812,15.187)"><path id="x210E" d="M499 88q-41 -46 -83.5 -73t-68.5 -27q-41 0 -19 98l52 225q10 43 8 59.5t-16 16.5q-37 0 -112 -65t-117 -135q-14 -42 -38 -179q-36 -7 -75 -20l-7 8l127 594q8 40 2.5 49t-35.5 9h-35l5 25q36 3 71.5 13t56.5 18t25 8q11 0 3 -38l-88 -417h2q77 102 195 167q44 24 79 24&#xA;q61 0 30 -130l-52 -220q-8 -33 4 -33q8 0 31 14.5t43 33.5z" /></g>

		
	
</svg> symmetries. By working under the hypothesis of self-similarity we find exact solutions for two different theoretical models, which are the Jordan-Brans-Dicke (JBD) with <svg     style="vertical-align:-3.56265pt;width:37.025002px;" id="M5" height="16.625" version="1.1" viewBox="0 0 37.025002 16.625" width="37.025002"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,12.138)"><use xlink:href="#x39B"/></g><g transform="matrix(.017,-0,0,-.017,11.724,12.138)"><path id="x28" d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" /></g><g transform="matrix(.017,-0,0,-.017,17.605,12.138)"><path id="x1D719" d="M542 242q0 -106 -80 -176.5t-192 -72.5l-55 -251l-6 -3q-18 7 -28 38t1 91l23 124q-85 16 -133.5 72.5t-48.5 137.5q0 95 62.5 159.5t166.5 97.5l14 -31q-77 -32 -115 -82.5t-38 -128.5q0 -63 31.5 -107t74.5 -59l125 597l56 43l16 -10l-40 -168q-9 -40 3 -45&#xA;q77 -33 120 -85.5t43 -140.5zM469 232q0 67 -37 115t-77 62l-76 -370q89 -4 139.5 52.5t50.5 140.5z" /></g><g transform="matrix(.017,-0,0,-.017,27.21,12.138)"><path id="x29" d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" /></g><g transform="matrix(.017,-0,0,-.017,33.091,12.138)"><path id="x2C" d="M95 130q31 0 61 -30t30 -78q0 -53 -38 -87.5t-93 -51.5l-11 29q77 31 77 85q0 26 -17.5 43t-44.5 24q-4 0 -8.5 6.5t-4.5 17.5q0 18 15 30t34 12z" /></g>

		
	
</svg> and the usual JBD model with potential <svg     style="vertical-align:-3.56265pt;width:34.462502px;" id="M6" height="16.625" version="1.1" viewBox="0 0 34.462502 16.625" width="34.462502"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,12.138)"><path id="x1D448" d="M751 650l-6 -28q-53 -1 -69 -12.5t-24 -38.5q-23 -85 -43 -192l-13 -69q-34 -181 -130 -262q-79 -65 -185 -65t-171 57q-87 77 -54 258l42 232q12 58 0.5 73t-75.5 19l8 28h263l-6 -28q-63 -5 -78 -18t-26 -74l-41 -226q-25 -135 22 -201t139 -66q99 0 161.5 68t91.5 217&#xA;l11 57q28 149 28 193q0 28 -19 38t-79 12l6 28h247z" /></g><g transform="matrix(.017,-0,0,-.017,13.033,12.138)"><use xlink:href="#x28"/></g><g transform="matrix(.017,-0,0,-.017,18.914,12.138)"><use xlink:href="#x1D719"/></g><g transform="matrix(.017,-0,0,-.017,28.518,12.138)"><use xlink:href="#x29"/></g>

		
	
</svg> (that mimics the behaviour of <svg     style="vertical-align:-3.56265pt;width:39.037498px;" id="M7" height="16.625" version="1.1" viewBox="0 0 39.037498 16.625" width="39.037498"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,12.138)"><use xlink:href="#x39B"/></g><g transform="matrix(.017,-0,0,-.017,11.724,12.138)"><use xlink:href="#x28"/></g><g transform="matrix(.017,-0,0,-.017,17.605,12.138)"><use xlink:href="#x1D719"/></g><g transform="matrix(.017,-0,0,-.017,27.21,12.138)"><use xlink:href="#x29"/></g><g transform="matrix(.017,-0,0,-.017,33.091,12.138)"><use xlink:href="#x29"/></g>

		
	
</svg>. We compare both theoretical models, and some physical and geometrical properties of the solutions are also discussed putting special emphasis on the study of the isotropization of the solutions.

J. A. Belinch&#xf3;n

Scalar-Tensor Bianchi VI Models

We develop a simple model for a self-gravitating spherically symmetric relativistic star which begins to collapse from an initially static configuration by dissipating energy in the form of radial heat flow. We utilize the model to show how local anisotropy affects the collapse rate and thermal behavior of gravitationally evolving systems.

Ranjan Sharma

Shyam Das

Collapse of a Relativistic Self-Gravitating Star with Radial Heat Flux: Impact of Anisotropic Stresses

We have developed the recent investigations on the second-order phase transition in the holographic superconductor using the probe limit for a nonlinear Maxwell field strength coupled to a massless scalar field. By analytical methods, based on the variational Sturm-Liouville minimization technique, we study the effects of the spacetime dimension and the nonlinearity parameter on the critical temperature and the scalar condensation of the dual operators on the boundary. Further, as a motivated result, we analytically deduce the DC conductivity in the low and zero temperatures regime. Especially in the zero temperature limit and in two dimensional toy model, we thoroughly compute the conductivity analytically. Our work clarifies more features of the holographic superconductors both in different space dimensions and on the effect of the nonlinearity in Maxwell's strength field.

Davood Momeni

Muhammad Raza

Ratbay Myrzakulov

More on Superconductors via Gauge/Gravity Duality with Nonlinear Maxwell Field

The gravitational field of conical mass distributions is formulated using the general theory of relativity. The gravitational metric tensor is constructed and applied to the motion of test particles and photons in this gravitational field. The expression for gravitational time dilation is found to have the same form as that in spherical, oblate spheroidal, and prolate spheroidal gravitational fields and hence confirms an earlier assertion that this gravitational phenomena is invariant in form with various mass distributions. It is shown using the pure radial equation of motion that as a test particle moves closer to the conical mass distribution along the radial direction, its radial speed decreases.

Chifu Ebenezer Ndikilar

Gravitational Fields of Conical Mass Distributions

The flat Friedmann universes filled by stiff fluid and a nonminimally
coupled material scalar field with polynomial potentials of the
fourth degree are considered in the framework of the
Einstein-Cartan theory. Exact general solution is obtained for arbitrary positive values of the coupling constant <svg     style="vertical-align:-2.57985pt;width:7.7375002px;" id="M1" height="15.9125" version="1.1" viewBox="0 0 7.7375002 15.9125" width="7.7375002"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,12.638)"><path id="x1D709" d="M425 682q0 -40 -49 -59q-36 -13 -110 -13q-31 -18 -52.5 -49.5t-21.5 -67.5q0 -34 17.5 -57.5t45.5 -28.5q63 15 97 15q18 0 18 -16q0 -13 -22 -36t-34 -23q-50 0 -93 8q-47 -20 -80.5 -66.5t-33.5 -96.5q0 -76 84 -103q33 -11 75 -21q101 -26 101 -93q0 -51 -39 -95.5&#xA;t-76 -68.5l-22 20q60 69 60 111q0 21 -14 34t-55 22q-21 4 -63 16q-68 19 -101.5 52.5t-33.5 96.5q0 125 157 206q-27 10 -46 36t-19 58q0 84 103 152q-43 3 -71.5 21t-28.5 45q0 37 65 59l17 -6q-9 -14 -9 -33q0 -21 17.5 -36t51.5 -19q82 53 147 53q18 0 18 -17z" /></g>

		
	
</svg>. A comparative analysis of the cosmological models with and without stiff fluid is carried out. Some effects of stiff fluid are
elucidated. It is shown that singular models with a de Sitter asymptotic and with the power-law <svg     style="vertical-align:-2.3205pt;width:34.637501px;" id="M2" height="19.5375" version="1.1" viewBox="0 0 34.637501 19.5375" width="34.637501"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,16.588)"><path id="x28" d="M300 -147l-18 -23q-106 71 -159 185.5t-53 254.5v1q0 139 53 252.5t159 186.5l18 -24q-74 -62 -115.5 -173.5t-41.5 -242.5q0 -130 41.5 -242.5t115.5 -174.5z" /></g><g transform="matrix(.017,-0,0,-.017,5.944,16.588)"><path id="x1D461" d="M324 430l-26 -36l-112 -4l-55 -265q-13 -66 7 -66q13 0 44.5 20t50.5 40l17 -24q-38 -40 -85.5 -73.5t-87.5 -33.5q-50 0 -21 138l55 262h-80l-2 8l25 34h66l25 99l78 63l10 -9l-37 -153h128z" /></g>

			<g transform="matrix(.012,-0,0,-.012,11.738,8.425)"><path id="x34" d="M456 178h-96v-72q0 -51 12.5 -62.5t72.5 -16.5v-27h-256v27q65 5 78 17t13 62v72h-260v28q182 271 300 426h40v-407h96v-47zM280 225v295h-2q-107 -148 -196 -295h198z" /></g><g transform="matrix(.012,-0,0,-.012,17.449,8.425)"><path id="x2F" d="M368 703l-264 -866h-60l265 866h59z" /></g><g transform="matrix(.012,-0,0,-.012,22.351,8.425)"><path id="x33" d="M285 378v-2q65 -13 102 -54.5t37 -97.5q0 -57 -30.5 -104.5t-74 -75t-85.5 -42t-72 -14.5q-31 0 -59.5 11t-40.5 23q-19 18 -16 36q1 16 23 33q13 10 24 0q58 -51 124 -51q55 0 88 40t33 112q0 64 -39 96.5t-88 32.5q-29 0 -64 -11l-6 29q77 25 118 57.5t41 84.5&#xA;q0 45 -26.5 69.5t-68.5 24.5q-67 0 -120 -79l-20 20l43 63q51 56 127 56h1q66 0 107 -37t41 -95q0 -42 -31 -71q-22 -23 -68 -54z" /></g>

			<g transform="matrix(.017,-0,0,-.017,28.688,16.588)"><path id="x29" d="M275 270q0 -296 -211 -440l-19 23q75 62 116.5 174t41.5 243t-42 243t-116 173l19 24q211 -144 211 -440z" /></g>

		
	
</svg> asymptotic at late times are possible. It is found that <svg     style="vertical-align:-2.57985pt;width:50.487499px;" id="M3" height="15.9125" version="1.1" viewBox="0 0 50.487499 15.9125" width="50.487499"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
			<g transform="matrix(.017,-0,0,-.017,.062,12.638)"><use xlink:href="#x1D709"/></g><g transform="matrix(.017,-0,0,-.017,12.387,12.638)"><path id="x3D" d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" /></g><g transform="matrix(.017,-0,0,-.017,27.091,12.638)"><use xlink:href="#x33"/></g><g transform="matrix(.017,-0,0,-.017,35.25,12.638)"><use xlink:href="#x2F"/></g><g transform="matrix(.017,-0,0,-.017,42.253,12.638)"><path id="x38" d="M249 635q70 0 116 -43t46 -105q0 -46 -28 -80q-22 -25 -80 -64q62 -35 97 -75t35 -99q0 -81 -63 -131t-135 -50q-83 0 -137.5 45.5t-54.5 123.5q0 52 45 95q29 28 89 64q-109 62 -109 155q0 66 50.5 115t128.5 49zM238 603q-42 0 -67.5 -31t-25.5 -72q0 -50 32.5 -79.5&#xA;t98.5 -62.5q61 48 61 124q0 59 -29.5 90t-69.5 31zM248 20q46 0 76.5 33.5t30.5 89.5q0 50 -39 85.5t-110 71.5q-81 -54 -81 -137q0 -67 35.5 -105t87.5 -38z" /></g>

		
	
</svg> is a specific value of the coupling constant. It is demonstrated that the bouncing models without the particle horizon and with an accelerated expansion by a de Sitter law of an evolution at late times are admissible.

Almaz Galiakhmetov

Stiff Fluid in Accelerated Universes with Torsion

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Journal of Gravity