A black hole isn't completely black. From its horizon, a faint thermal glow constantly seeps out, like steam rising from a cooling cup of tea. The temperature of this glow depends on the strength of gravity at the surface. But if particles carry very high energy, the usual formulas can mislead — because at energies near the Planck scale, spacetime itself starts to behave differently.
This new work compares two approaches to this problem. The first treats the particle as if it were in a small laboratory freely falling near the horizon. The second treats the geometry of space as if it changes with the particle's energy, like a city map being redrawn for a pedestrian versus a train. It turns out that for a spherically symmetric black hole, both approaches give the same temperature shift when the particle energy is fixed at a reasonable value.
For simple models of deformed relativity, the correction vanishes altogether. For a more general case with two parameters, the temperature can become slightly lower or higher than usual, but the difference is always proportional to the ratio of the particle energy to the Planck energy. For macroscopic black holes, this ratio is minuscule, and the effect is lost in the noise. It only becomes noticeable for black holes the size of an atomic nucleus, where particle energies are comparable to the Planck scale.
Thus, different ways of accounting for ultra-high energies near a black hole lead to the same answer for the temperature. This gives hope that at least the thermal properties of such objects can be described uniformly, despite our incomplete knowledge of quantum gravity.
as written by the authors arXiv:2602.15216
Doubly Special Relativity (DSR) deforms special-relativistic kinematics by introducing an invariant Planck energy scale $$E_{\mathrm{Pl}}$$ alongside the speed of light, while preserving the relativity principle. A key issue in curved spacetimes, particularly black-hole thermodynamics, is the operational meaning of the ``energy'' in modified dispersion relations (MDRs). We compare two common implementations in a controlled static black-hole spacetime: (i) MDRs in local orthonormal frames on a fixed background geometry, and (ii) the rainbow-metric approach with an energy-dependent family of effective metrics. For static, spherically symmetric horizons and using a consistent finite operational energy scale $$E_\star$$ for emitted quanta, both yield the same near-horizon temperature rescaling \[ T(E_\star)=T_0\,\frac{g(E_\star/E_{\mathrm{Pl}})}{f(E_\star/E_{\mathrm{Pl}})}, \quad T_0=\kappa_0/(2\pi), \] where $$f$$ and $$g$$ are the standard rainbow/MDR functions. This establishes a universality of the tunneling/surface-gravity temperature, with deformation entering solely via the ratio $$g/f$$. We illustrate for Amelino-Camelia MDR and Magueijo-Smolin DSR (where $$f=g$$, implying $$T(E_\star)=T_0$$). Extending to a two-parameter generalized DSR (G-DSR) with leading parameters $$(\alpha_2, \Delta\alpha)$$, we obtain \[ T_{\mathrm{GDRS}}(E_\star) = T_0 \sqrt{\frac{1-2\Delta\alpha\,(E_\star/E_{\mathrm{Pl}})}{1-2\alpha_2\,(E_\star/E_{\mathrm{Pl}})}} \simeq T_0 [1 - (\Delta\alpha - \alpha_2) E_\star/E_{\mathrm{Pl}}]. \] We discuss the role of $$\Delta\alpha - \alpha_2$$ (vanishing correction for the symmetric $$\Delta\alpha=\alpha_2$$ subfamily) and note that further model dependence arises from phase-space measures, greybody factors, and non-linear composition laws. Corrections are strongly suppressed for macroscopic black holes and become relevant only near the Planck regime.
The Planck energy is roughly the energy carried by a flying mosquito. Only, in a mosquito, that energy is spread over a huge number of particles, whereas here it's squeezed into a single one.
In Peter Watts's novel "Firefly," the crew of a ship encounters quantum effects near a black hole, where familiar physics breaks down.