Analytical approach for calculating shadow of dynamical black hole
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918326284845056 |
|---|---|
| author | Vertogradov, Vitalii Övgün, Ali |
| author_facet | Vertogradov, Vitalii Övgün, Ali |
| contents | We develop a compact and transparent framework for photon dynamics and shadow formation in slowly evolving, spherically symmetric spacetimes. Starting from the Eddington-Finkelstein action, we derive a force-decomposed radial equation in which the radial acceleration splits into an induced term sourced by mass variation, a centrifugal term, and a purely general-relativistic correction. A key result is a gauge-invariant energy-flux relation, $d(E^2)/dv=-Λ/r$, with $Λ\equiv \varepsilon\,\dot M\,\dot v^2$, which controls how time dependence modifies the canonical energy of null geodesics. In the adiabatic regime we obtain an explicit first-order shift of the photon-sphere radius, $r_{ph}(v)=r_0-a_i/(a_g'+a_c')$, and connect it to the observable shadow through the evolving critical impact parameter, $b_{\rm crit}(v)=\sqrt{r_{ph}(v)^2/f(r_{ph}(v))}$. For Vaidya spacetimes this predicts that accretion ($\dot M>0$) expands the photon sphere and increases the shadow angle, whereas mass loss has the opposite effect. Our formulation refines classic force-balance ideas to dynamical settings, provides a constructive link to time-dependent photon surfaces, and yields simple, observer-ready expressions for the evolution of the shadow. The framework offers a baseline for confronting time-variable horizon-scale imaging with dynamical inflow/outflow models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10930 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analytical approach for calculating shadow of dynamical black hole Vertogradov, Vitalii Övgün, Ali General Relativity and Quantum Cosmology We develop a compact and transparent framework for photon dynamics and shadow formation in slowly evolving, spherically symmetric spacetimes. Starting from the Eddington-Finkelstein action, we derive a force-decomposed radial equation in which the radial acceleration splits into an induced term sourced by mass variation, a centrifugal term, and a purely general-relativistic correction. A key result is a gauge-invariant energy-flux relation, $d(E^2)/dv=-Λ/r$, with $Λ\equiv \varepsilon\,\dot M\,\dot v^2$, which controls how time dependence modifies the canonical energy of null geodesics. In the adiabatic regime we obtain an explicit first-order shift of the photon-sphere radius, $r_{ph}(v)=r_0-a_i/(a_g'+a_c')$, and connect it to the observable shadow through the evolving critical impact parameter, $b_{\rm crit}(v)=\sqrt{r_{ph}(v)^2/f(r_{ph}(v))}$. For Vaidya spacetimes this predicts that accretion ($\dot M>0$) expands the photon sphere and increases the shadow angle, whereas mass loss has the opposite effect. Our formulation refines classic force-balance ideas to dynamical settings, provides a constructive link to time-dependent photon surfaces, and yields simple, observer-ready expressions for the evolution of the shadow. The framework offers a baseline for confronting time-variable horizon-scale imaging with dynamical inflow/outflow models. |
| title | Analytical approach for calculating shadow of dynamical black hole |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2412.10930 |