Black Hole Solutions and Pressure Terms in Induced Gravity with Higgs Potential

TL;DR

This paper explores black hole solutions in a scalar-tensor gravity theory with Higgs potential, analyzing their properties, horizons, and potential links to galactic rotation curves, highlighting the influence of pressure and scalar fields.

Contribution

It introduces a series-expansion method to derive black hole solutions with Higgs potential and examines their physical implications and connection to galactic dynamics.

Findings

Derivation of Reissner–Nordström-like and Schwarzschild black hole solutions.

Dependence of black hole horizons on pressure and scalar field excitations.

Potential explanation for flat rotation curves via scalar field interactions.

Abstract

We study the quintessential properties of the Black Hole solutions in a scalar--tensor theory of gravity with Higgs potential in view of the static and spherically symmetric line element. In view of our earlier results, Reissner--Nordstr\"om-like and Schwarzschild Black Hole solutions are derived with the introduction of a series-expansion method to solve the field equations without and with Higgs field mass. The physical consequences of the Black Hole solutions and the solutions obtained in the weak field limit are discussed in detail by the virtue of the equation-of-state parameter, the scalar-field excitations and the geodesic motion. The appearance of naked singularities is also discussed together with the dependence of Black Hole horizons on the field excitations, which are themselves dependent on pressure terms which effectively screen the mass terms. A possible connection to flat rotation curves following the interaction with the scalar field is also presented in the weak field limit of gravity, together with a discussion of dynamical effects of scalar fields and pressure terms on mass.