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Register a new userNon-trivial static, spherically symmetric vacuum solution in a non-conservative theory of gravity
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We analyse the vacuum static spherically symmetric space-time for a specific class of non-conservative theories of gravity based on the Rastalls theory. We obtain a new vacuum solution which has the same structure as the Schwarzschild-de Sitter solution in the General Relativity theory obtained with a cosmological constant playing the r^ole of source. We further discuss the structure (in particular, the coupling to matter fields) and some cosmological aspects of the underline non-conservative theory
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By using of the Euler-Lagrange equations, we find a static spherically symmetric solution in the Einstein-aether theory with the coupling constants restricted. The solution is similar to the Reissner-Nordstrom solution in that it has an inner Cauchy horizon and an outer black hole event horizon. But a remarkable difference from the Reissner-Nordstrom solution is that it is not asymptotically flat but approaches a two dimensional sphere. The resulting electric potential is regular in the whole spacetime except for the curvature singularity. On the other hand, the magnetic potential is divergent on both Cauchy horizon and the outer event horizon.
We show, in detail, that the only non-trivial black hole (BH) solutions for a neutral as well as a charged spherically symmetric space-times, using the class ${textit F(R)}={textit R}pm{textit F_1 (R)} $, must-have metric potentials in the form $h(r)=frac{1}{2}-frac{2M}{r}$ and $h(r)=frac{1}{2}-frac{2M}{r}+frac{q^2}{r^2}$. These BHs have a non-trivial form of Ricci scalar, i.e., $R=frac{1}{r^2}$ and the form of ${textit F_1 (R)}=mpfrac{sqrt{textit R}} {3M} $. We repeat the same procedure for (Anti-)de Sitter, (A)dS, space-time and got the metric potentials of neutral as well as charged in the form $h(r)=frac{1}{2}-frac{2M}{r}-frac{2Lambda r^2} {3} $ and $h(r)=frac{1}{2}-frac{2M}{r}+frac{q^2}{r^2}-frac{2Lambda r^2} {3} $, respectively. The Ricci scalar of the (A)dS space-times has the form ${textit R}=frac{1+8r^2Lambda}{r^2}$ and the form of ${textit F_1(R)}=mpfrac{textit 2sqrt{R-8Lambda}}{3M}$. We calculate the thermodynamical quantities, Hawking temperature, entropy, quasi-local energy, and Gibbs-free energy for all the derived BHs, that behaves asymptotically as flat and (A)dS, and show that they give acceptable physical thermodynamical quantities consistent with the literature. Finally, we prove the validity of the first law of thermodynamics for those BHs.
We continue the study of the non-metric theory of gravity introduced in hep-th/0611182 and gr-qc/0703002 and obtain its general spherically symmetric vacuum solution. It respects the analog of the Birkhoff theorem, i.e., the vacuum spherically symmetric solution is necessarily static. As in general relativity, the spherically symmetric solution is seen to describe a black hole. The exterior geometry is essentially the same as in the Schwarzschild case, with power-law corrections to the Newtonian potential. The behavior inside the black-hole region is different from the Schwarzschild case in that the usual spacetime singularity gets replaced by a singular surface of a new type, where all basic fields of the theory remain finite but metric ceases to exist. The theory does not admit arbitrarily small black holes: for small objects, the curvature on the would-be horizon is so strong that non-metric modifications prevent the horizon from being formed. The theory allows for modifications of gravity of very interesting nature. We discuss three physical effects, namely, (i) correction to Newtons law in the neighborhood of the source, (ii) renormalization of effective gravitational and cosmological constants at large distances from the source, and (iii) additional redshift factor between spatial regions of different curvature. The first two effects can be responsible, respectively, for the observed anomaly in the acceleration of the Pioneer spacecraft and for the alleged missing mass in spiral galaxies and other astrophysical objects. The third effect can be used to propose a non-cosmological explanation of high redshifts of quasars and gamma-ray bursts.
We investigate the proper projective collineation in non-static spherically symmetric space-times using direct integration and algebraic techniques. Studying projective collineation in the above space-times, it is shown that the space-times which admit proper projective collineations turn out to be very special classes of static spherically symmetric space-times.
We examine in this paper the possibility of finding exact solutions for Teleparallel Gravity (TG) of the type of spherically symmetric Lema^i tre-Tolman-Bondi (LTB) dust models. We apply to the LTB metric, as obtained from the Schwarzschild solution in General Relativity, the formalism of Teleparallel Gravity in its extension to $f(T,B)$ models. An exact LTB solution is obtained that is compatible with a specific $f(T,B)$ model that seems to be appropriate to fit observations when applied to standard spatially flat Robertson-Walker geometry.
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