General form of $f(R)$ and $(2+1)$-dimensional charge/non-charge black hole solutions
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912594310201344 |
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| author | Nashed, G. G. L. |
| author_facet | Nashed, G. G. L. |
| contents | We introduce novel black hole (BH) solutions, charge/non-charge, within the framework of $f(R)$ gravity, a theory that does not inherently include a cosmological constant, using equal/diffirent metric ansatzs. Remarkably, these solutions exhibit asymptotically Anti-de Sitter (AdS) or de Sitter (dS) behavior, depending on their parameter values. Unlike the BTZ solutions of General Relativity, which feature a causal singularity and constant scalar invariants, our solutions display strong spacetime singularities, as shown by their scalar invariants. We construct $f(R)$ functions that behave as polynomial functions, emphasizing the unique nature of these solutions. We demonstrate the stability of these solutions in two ways: first, by showing that their heat capacity is positive, which ensures thermodynamic stability; and second, by proving that the second derivative of $f(R)$ is positive, meeting the Ostrogradski criterion for dynamical stability. Furthermore, the solutions satisfy the first law of thermodynamics, confirming their consistency with fundamental thermodynamic principles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_15282 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | General form of $f(R)$ and $(2+1)$-dimensional charge/non-charge black hole solutions Nashed, G. G. L. General Relativity and Quantum Cosmology High Energy Physics - Theory We introduce novel black hole (BH) solutions, charge/non-charge, within the framework of $f(R)$ gravity, a theory that does not inherently include a cosmological constant, using equal/diffirent metric ansatzs. Remarkably, these solutions exhibit asymptotically Anti-de Sitter (AdS) or de Sitter (dS) behavior, depending on their parameter values. Unlike the BTZ solutions of General Relativity, which feature a causal singularity and constant scalar invariants, our solutions display strong spacetime singularities, as shown by their scalar invariants. We construct $f(R)$ functions that behave as polynomial functions, emphasizing the unique nature of these solutions. We demonstrate the stability of these solutions in two ways: first, by showing that their heat capacity is positive, which ensures thermodynamic stability; and second, by proving that the second derivative of $f(R)$ is positive, meeting the Ostrogradski criterion for dynamical stability. Furthermore, the solutions satisfy the first law of thermodynamics, confirming their consistency with fundamental thermodynamic principles. |
| title | General form of $f(R)$ and $(2+1)$-dimensional charge/non-charge black hole solutions |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2509.15282 |