We analyze the time evolution of a spherically-symmetric collapsing matter from the point of view that black holes evaporate by nature. We consider conformal matters and solve the semi-classical Einstein equation $G_{\mu \nu }=8\pi G\langle T_{\mu \nu }\rangle$ by using the four-dimensional Weyl anomaly with a large c coefficient. Here, $\langle T_{\mu \nu }\rangle$ contains the contribution from both the collapsing matter and Hawking radiation. The solution indicates that the collapsing matter forms a dense object and evaporates without horizon or singularity, and it has a surface, but looks like an ordinary black hole from the outside. Any object we recognize as a black hole should be such an object.

Static, spherically symmetric black hole solutions to the semi-classical Einstein equation are studied, including the effect of the quantum energy-momentum tensor for conformal matters with 4D Weyl anomaly. Through both perturbative and non-perturbative methods, we show that the quantum effect can play a crucial role in shaping the nearhorizon geometry, and that the existence of the horizon requires fine-tuning.

We study analytically the spacetime geometry of the black-hole formation and evaporation. As a simplest model of the collapse, we consider a spherical thin shell, and take the backreaction from the negative energy of the quantum vacuum state. For definiteness, we will focus on quantum effects of s-waves. We obtain an analytic solution of the semiclassical Einstein equation for this model, that provides an overall description of the black hole geometry form the formation to evaporation. As an application of this result, we find its interesting implication that, after the collapsing shell enters the apparent horizon, the proper distance between the shell and the horizon remains as small as the Planck length even when the difference in their areal radii is of the same order as the Schwarzschild radius. The position of the shell would be regarded as the same place to the apparent horizon in the semiclassical regime of gravity.

We describe 4D evaporating black holes as quantum field configurations by solving the semi-classical Einstein equation $G_{\mu \nu }=8\pi G⟨\psi |T_{\mu \nu }|\psi ⟩$ and quantum matter fields in a self-consistent manner. As the matter fields, we consider N massless free scalar fields (N is large). We find a spherically symmetric self-consistent solution of the metric $g_{\mu \nu }$ and the state $|\psi ⟩$ . Here, $g_{\mu \nu }$ is locally $Ad{S}_2\times S^2$ geometry, and $|\psi ⟩$ provides $⟨\psi |T_{\mu \nu }|\psi ⟩=⟨0|T_{\mu \nu }|0⟩+T_{\mu \nu }^{\left(\psi \right)}$ , where $|0⟩$ is the ground state of the matter fields in the metric and $T_{\mu \nu }^{\left(\psi \right)}$ consists of the excitation of s-waves that describe the collapsing matter and Hawking radiation with the ingoing negative energy flow. This object is supported by a large tangential pressure $⟨0\left|{T^{\theta }}_{\theta }\right|0⟩$ due to the vacuum fluctuation of the bound modes with large angular momenta $l\gg 1$ . This describes the interior of the black hole when the back reaction of the evaporation is taken into account. In this picture, the black hole is a compact object with a surface (instead of horizon) that looks like a conventional black hole from the outside and eventually evaporates without a singularity. If we count the number of configurations $\left\{\right|\psi ⟩\}$ that satisfy the self-consistent equation, we reproduce the area law of the entropy. This tells that the information is carried by the s-waves inside the black hole. $|\psi ⟩$ also describes the process that the negative ingoing energy flow created with Hawking radiation is superposed on the collapsing matter to decrease the total energy while the total energy density remains positive. Finally, as a special case, we consider conformal matter fields and show that the interior metric is determined by the matter content of the theory, which leads to a new constraint to the matter contents for the black hole to evaporate.

In the background of a gravitational collapse, we compute the transition amplitudes for the creation of particles for distant observers due to higher-derivative interactions in addition to Hawking radiation. The amplitudes grow exponentially with time and become of order 1 when the collapsing matter is about a Planck length outside the horizon. As a result, the effective theory breaks down at the scrambling time, invalidating its prediction of Hawking radiation. Planckian physics comes into play to decide the fate of black-hole evaporation.

Assuming that the vacuum energy-momentum tensor is not exceptionally large, we consider 4D evaporating black holes with spherical symmetry and evaluate the proper distance $\mathrm{\Delta }L$ between the timelike apparent horizon and the surface of the collapsing matter after it has entered the apparent horizon. We show that $\mathrm{\Delta }L$ can never be larger than $\mathcal{O}(n^{3/2}{\ell }_p)$ when the black hole has evaporated to $1/n$ of its initial mass, as long as $n\ll a^{2/3}/{\ell }_p^{2/3}$ (where $a$ is the Schwarzschild radius and ${\ell }_p$ is the Planck length). For example, the distance between the matter and the apparent horizon must be Planckian at the Page time.