Black holes with Lagrange multiplier and potential in mimetic-like gravitational theory: multi-horizon black holes

Abstract

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 literature that mimetic theory coincides with GR \cite{Nashed:2018qag}. In the second case, we derive a solution with a constant value of the {\bf potential} and a dynamical value of the Lagrange multiplier. This solution has no horizon and therefore the obtained spacetime does not correspond to the BH. In this solution, there appears the region of the Euclidian signature where the signature of the diagonal components of the metric is $(+,+,+,+)$ or the region with two times where the signature is $(+,+,-,-)$. Finally, we derive a BH solution with non-vanishing values of the Lagrange multiplier, {\bf potential}, and {\bf mimetic-like scalar field}. This BH shows a soft singularity compared with the Einstein BH solution. The relevant physics of the third case is discussed by showing their behavior of the metric potential at infinity, calculating their energy conditions, and study their thermodynamical quantities. We give a brief discussion on how our third case can generate a BH with three horizons as in the de Sitter-Reissner-Nordström black hole spacetime, where the largest horizon is the cosmological one and two correspond to the outer and inner horizons of the BH. Even in the third case, there appears the region of the Euclidian signature or the region with two times.

14 pages, 12 figures. arXiv admin note: text overlap with arXiv:2107.13550

References in corpus (36)

• Mimetic gravity: a review of recent developments and applications to cosmology and astrophysics
• Cosmology with Mimetic Matter
• Mimetic $F(R)$ gravity: inflation, dark energy and bounce
• Higher dimensional charged $f(R)$ black holes
• Thermodynamics of apparent horizon and modified Friedman equations
• Disformal Transformations, Veiled General Relativity and Mimetic Gravity
• Dark energy from modified gravity with Lagrange multipliers
• Thermodynamics of higher dimensional topological charged AdS black branes in dilaton gravity
• Imperfect Dark Matter
• Topological Born-Infeld-dilaton black holes
• Extended matter bounce scenario in ghost free $f(R,\mathcal{G})$ gravity compatible with GW170817
• Cosmological perturbations in mimetic matter model
• On the Energy Issue for a Class of Modified Higher Order Gravity Black Hole Solutions
• Viable Mimetic Completion of Unified Inflation-Dark Energy Evolution in Modified Gravity
• Spherically symmetric black holes with electric and magnetic charge in extended gravity: Physical properties, causal structure, and stability analysis in Einstein's and Jordan's frames
• Ghost-Free $F(R)$ Gravity with Lagrange Multiplier Constraint
• Generalized teleparallel cosmology and initial singularity crossing
• Thermodynamics of rotating solutions in (n+1)-dimensional Einstein-Maxwell-dilaton gravity
• Schwarzschild solution in extended teleparallel gravity
• Hamiltonian analysis of mimetic scalar gravity revisited
• Anisotropic compact stars in the mimetic gravitational theory
• Non-singular Bounce Cosmology from Lagrange Multiplier $F(R)$ Gravity
• Dark Energy Oscillations in Mimetic $F(R)$ Gravity
• Mimetic Euler-Heisenberg theory, charged solutions and multi-horizon black holes
• Thick branes with inner structure in mimetic $f(R)$ gravity
• Aspects of Late-time Evolution in Mimetic $F(R)$ Gravity
• New rotating AdS/dS black holes in $\mathrm{f}(\mathrm{R})$ gravity
• Reconstruction of mimetic gravity in a non-singular bouncing universe from quantum gravity
• Mimetic Black Strings
• Mimetic gravity in $(2+1)$-dimensions
• Mimetic Inflation
• Massive mimetic cosmology
• Mimetic DBI Inflation in Confrontation with Planck2018 data
• Viable non-singular cosmic bounce in holonomy improved F(R) gravity endowed with a Lagrange multiplier
• Quadratic and cubic spherically symmetric black holes in the modified teleparallel equivalent of general relativity: Energy and thermodynamics
• De Sitter and power-law solutions in some models of modified gravity

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