We present two new classes of black string solutions in the context of mimetic gravity. The horizon topology of these solutions can be either a flat $T^2$ torus with topology $S^1 \times S^1$, or a standard cylindrical model with topology $R\times S^1$. The first class describes uncharged rotating black string which its asymptotic behavior is a quotient of anti-de Sitter (AdS) space, while the second class represents asymptotically AdS charged rotating black string. We study the casual structure and physical properties of these spacetimes and calculate, the entropy, electric charge, mass and angular momentum per unit length of rotating black strings.
We show that the mimetic theory with the constraint $g^{ρσ}\partial_ρϕ\partial_σϕ=1$ cannot realize the black hole geometry with the horizon(s). To overcome such issue, we may change the mimetic constraint a little bit by $ω(ϕ) g^{ρσ}\partial_ρϕ\partial_σϕ=-1,$ where $ω(ϕ)$ is a function of the scalar field $ϕ$. As an example, we consider $(2+1)$-dimensional mimetic gravity with the mimetic potential and construct black hole (BH) solutions by using this modified constraint. We study three different classes: In the first class, we assume the Lagrange multiplier and mimetic potential are vanishi…
In this paper, we look for the vacuum static spherically symmetric solution in the mimetic gravity scenario based on the conformal invariance principle. The trivial solution is a stealth Schwarzschild black hole with scalar hair where the mimetic field does not contribute to the background. However, a solution with two naked singularities shows up when the mimetic scalar field contributes to the background. We show that one of these singularities is the same as the singularity at the center of standard Schwarzschild black hole while the other appears due to caustics formation. However, we cons…
The vacuum, static, and spherically symmetric solutions in the mimetic Born-Infeld gravity are studied. The mimetic Born-Infeld gravity is a reformulation of the Eddington-inspired-Born-Infeld (EiBI) model under the mimetic approach. Due to the mimetic field, the theory contains non-trivial vacuum solutions different from those in Einstein gravity. We find that with the existence of the mimetic field, the spacelike singularity inside a Schwarzschild black hole could be altered to a lightlike singularity, even though the curvature invariants still diverge at the singularity. Furthermore, in thi…
In this paper, we employ the {\bf mimetic-like} field equations coupled with the Lagrange multiplier and %mimetic {\bf potential} to derive non-trivial spherically symmetric black hole (BH) solutions. We divided this study into three cases: The first one in which we take the Lagrange multiplier and %mimetic {\bf the potential} to have vanishing value and derive a BH solution that completely coincides with the BH of the Einstein general relativity despite the non-vanishing value of the {\bf mimetic-like scalar field}. The first case is completely consistent with the previous studies in the lite…
In this brief note we investigate the conditions under which a Schwarzschild de Sitter black hole spacetime is a solution of the mimetic $F(R)$ gravity with Lagrange multiplier and potential. As we demonstrate, the resulting mimetic $F(R)$ gravity is a slight modification of the ordinary $F(R)$ gravity case, however the resulting perturbation equations are not in all cases identical to the ordinary $F(R)$ gravity case. In the latter case, the perturbation equations are identical to the ones corresponding to the Reissner-Nordström anti-de Sitter black hole.
One of the most important achievements in general relativity has been discovery of the $(2+1)$-dimensional black hole solutions of Einstein gravity in anti-de Sitter (AdS) spacetime [Phys. Rev. Lett. {\bf69}, 1849 (1992)]. In this paper, we construct, for the first time, the $(2+1)$-dimensional solutions of mimetic theory of gravity. These solutions may provide a powerful background to investigate the physical properties of mimetic gravity and examine its viability in lower spacetime dimensions. In particular, some physical properties of stationary black hole solutions of this theory in the pr…
We construct several new classes of black hole (BH) solutions in the context of the mimetic Euler-Heisenberg theory. We separately derive three differently charged BH solutions and their relevant mimetic forms. We show that the asymptotic form of all BH solutions behaves like a flat spacetime. These BHs, either with/without cosmological constant, have the non constant Ricci scalar, due to the contribution of the Euler-Heisenberg parameter, which means that they are not solution to standard or mimetic $f(R)$ gravitational theory without the Euler-Heisenberg non-linear electrodynamics and at the…
Reissner-Nordström Black Holes in Mimetic $F(R)$ Gravity
本文研究了在什么条件下Reissner-Nordström-anti de Sitter黑洞可以是具有Lagrange乘子和模拟标量势的真空模拟$F(R)$引力的解.正如我们所证明的，在模拟$F(R)$重力情况下得到的图像与普通$F(R)$重力情况相比是不同的，这两种描述导致了一组不同的约束，这些约束需要保持正确。我们还研究了在模拟$F(R)$引力情形下，对于Reissner-Nordström-anti de Sitter黑洞度规，在一阶扰动变量下的度规扰动.有趣的是，得到的方程与普通$F(R)$引力Reissner-Nordström-anti de Sitter黑洞的方程是相同的，至少在一阶上是相同的。我们把这个特征归因于Reissner-Nordström-anti de Sitter度量的特殊形式，并且我们推测在哪些情况下模仿和非模仿的情况之间可能存在差异。由于这两种情况下的扰动方程是相同的，所以在模拟$F(R)$引力的情况下也可能存在黑洞不稳定性，这可以解释为黑洞的反蒸发。
The recently proposed theory of "Asymptotically Free Mimetic Gravity" is extended to the general non-homogeneous, spatially non-flat case. We present a modified theory of gravity which is free of higher derivatives of the metric. In this theory asymptotic freedom of gravity implies the existence of a minimal black hole with vanishing Hawking temperature. Introducing a spatial curvature dependent potential, we moreover obtain non-singular, bouncing modifications of spatially non-flat Friedmann and Bianchi universes.
In mimetic gravity, we derive $D$-dimension charged black hole solutions having flat or cylindrical horizons with zero curvature boundary. The asymptotic behaviours of these black holes behave as (A)dS. We study both linear and nonlinear forms of the Maxwell field equations in two separate contexts. For the nonlinear case, we derive a new solution having a metric with monopole, dipole and quadrupole terms. The most interesting feature of this black hole is that its dipole and quadruple terms are related by a constant. However, the solution reduces to the linear case of the Maxwell field equati…
We propose a new $\barμ$-scheme Hamiltonian effective dynamics in the spherical symmetric sector of Loop Quantum Gravity (LQG). The effective dynamics is generally covariant as derived from a covariant Lagrangian. The Lagrangian belongs to the class of extended mimetic gravity Lagrangians in 4 dimensions. We apply the effective dynamics to both cosmology and black hole. The effective dynamics reproduces the non-singular Loop-Quantum-Cosmology (LQC) effective dynamics. From the effective dynamics, we obtain the non-singular black hole solution, which has a killing symmetry in addition to the sp…
We construct some new classes of topological black hole solutions in the context of mimetic gravity. We study the uncharged and charged black holes, separately. In the absence of a potential for the mimetic field, our solutions can address the flat rotation curves of spiral galaxies and alleviate the dark matter problem without invoking any kind of particle dark matter. Thus, mimetic gravity can provide a theoretical background for understanding flat galactic rotation curves through modification of the Schwarzschild spacetime. We also investigate the casual structure and physical properties of…
The dynamics of the vacuum Kantowski-Sachs space-time are studied in the so-called limiting curvature mimetic gravity theory. It is shown that in this theory the vacuum Kantowski-Sachs space-time is always singular. While the departures from general relativity due to the limiting curvature mimetic theory do provide an upper bound on the magnitude of the expansion scalar, both its rate of oscillations and the magnitude of the directional Hubble rates increase without bound and cause curvature invariants to diverge. Also, since the radial scale factor does not vanish in finite (past) time, in th…
We find new solutions to the Einstein-Maxwell equations in the presence of mimetic field in $ D $ dimensions, all of which are asymptotically Antide Sitter. We derive the solutions in five-dimensional spacetime, in detail. By extending the calculations to six and seven dimensions, we obtain a general form for solutions in dimensions larger than four. The results describe electrically charged static and rotating solutions, which have spherical, toroidal or cylindrical horizons. The solutions, depending on their global identifications, can be regarded as black holes, or black strings/branes. Som…
We revisit the non-singular black hole solution in (extended) mimetic gravity with a limiting curvature from a Hamiltonian point of view. We introduce a parameterization of the phase space which allows us to describe fully the Hamiltonian structure of the theory. We write down the equations of motion that we solve in the regime deep inside the black hole, and we recover that the black hole has no singularity, due to the limiting curvature mechanism. Then, we study the relation between such black holes and effective polymer black holes which have been introduced in the context of loop quantum g…
We show that in asymptotically free mimetic gravity with limiting curvature the black hole singularity can be resolved and replaced by a static patch of de Sitter space. As a result of Hawking evaporation of these non-singular black holes, there remain stable remnants with vanishing Hawking temperature.
The black string solution is a model of black holes in (3+1) dimensions that can be related to the BTZ (2+1) dimensions black hole solution. This object can be seen as a cylindrical black hole. In this work it is considered the black string Hawking temperature obtained by the Hamilton-Jacobi method and a description of a system composed by a black string and a thermal reservoir, considering the thermal equilibrium state.
I was asked to give a brief review of the black hole-string correspondence as a warm-up for a longer SITP-group discussion of a recent paper by Chen, Maldacena, and Witten. Here are my notes in written form.
We study the recent claim that black NS5-branes are filled with folded strings. We calculate, in the near-extremal case, the number of folded strings at the black fivebranes interior, using different approaches, and get the exact same answer. The backreaction of the folded strings leads us to argue that the interior of the black fivebrane is AdS_2 (times a compact manifold) and that infalling matter cannot reach the interior, due to a shock wave at the horizon. These considerations also suggest a novel insight into the black fivebranes entropy.
We study black strings/funnels and other black hole configurations in AdS that correspond to different phases of the dual CFT in black hole backgrounds, employing different approaches at large $D$. We assemble the phase diagram of uniform and non-uniform black strings/funnels and study their dynamical stability. We also construct flowing horizons. Many of our results are available analytically, though some are only known numerically.
It is known that homogenous black strings in flat spacetime are unstable under long wavelength perturbations. Recently, by including scalar fields that depend on the extended coordinates only, homogenous black strings have been constructed in the presence of a negative cosmological constant, therefore implying that generic perturbations will contain both metric and scalar fluctuations. Here we show that for such generic perturbations homogeneous black strings with a negative cosmological constant are perturbatively stable at linear level, regardless the size of the Schwarzschild-AdS black hole…
