Gravitation Due to Scalar Potentials and Black Holes

Abstract In this paper we present a class of models in order to explain the production of Primordial Black Holes (PBHs) and Gravitational Waves (GWs) in the Universe. These models are based on no-scale theory. By breaking the SU(2,1)/SU(2)×U(1) symmetry we fix one of the two chiral fields and we derive effective scalar potentials which are capable of generating PBHs and GWs. As it is known in the literature there is an important unification of the no-scale models, which leads to the Starobinsky effective scalar potential based on the coset SU(2,1)/SU(2)×U(1). We use this unification in order to additionally explain the generation of PBHs and GWs. Concretely, we modify well-known superpotentials, which reduce to Starobinsky-like effective scalar potentials. Thus, we derive scalar potentials which, on the one hand, explain the production of PBHs and GWs and, on the other hand, they conserve the transformation laws, which yield from the parametrization of the coset SU(2,1)/SU(2)×U(1) as well as the unification between the models which are yielded this coset. We numerically evaluate the scalar power spectra with the effective scalar potential based on this theory. Furthermore, we evaluate the fractional abundances of PBHs by comparing two methods the Press–Schechter approach and the peak theory, while focusing on explaining the dark matter in the Universe. By using the resulting scalar power spectrum we evaluate the amount of GWs. All models are in complete consistence with Planck constraints.

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The FL bound and its phenomenological implications

Journal of High Energy Physics ◽

10.1007/jhep10(2021)009 ◽

2021 ◽

Vol 2021 (10) ◽

Author(s):

Miguel Montero ◽

Cumrun Vafa ◽

Thomas Van Riet ◽

Gerben Venken

Keyword(s):

Black Holes ◽

Local Minimum ◽

Charged Particles ◽

Higgs Potential ◽

De Sitter ◽

Throat Region ◽

Weak Force ◽

The Masses ◽

Scalar Potentials ◽

Matter Fields

Abstract Demanding that charged Nariai black holes in (quasi-)de Sitter space decay without becoming super-extremal implies a lower bound on the masses of charged particles, known as the Festina Lente (FL) bound. In this paper we fix the $$ \mathcal{O}(1) $$ O 1 constant in the bound and elucidate various aspects of it, as well as extensions to d > 4 and to situations with scalar potentials and dilatonic couplings. We also discuss phenomenological implications of FL including an explanation of why the Higgs potential cannot have a local minimum at the origin, thus explaining why the weak force must be broken. For constructions of meta-stable dS involving anti-brane uplift scenarios, even though the throat region is consistent with FL, the bound implies that we cannot have any light charged matter fields coming from any far away region in the compactified geometry, contrary to the fact that they are typically expected to arise in these scenarios. This strongly suggests that introduction of warped anti-branes in the throat cannot be decoupled from the bulk dynamics as is commonly assumed. Finally, we provide some evidence that in certain situations the FL bound can have implications even with gravity decoupled and illustrate this in the context of non-compact throats.

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No inner-horizon theorem for black holes with charged scalar hairs

Journal of High Energy Physics ◽

10.1007/jhep03(2021)263 ◽

2021 ◽

Vol 2021 (3) ◽

Author(s):

Rong-Gen Cai ◽

Li Li ◽

Run-Qiu Yang

Keyword(s):

Black Holes ◽

Scalar Potential ◽

Gravitational Theory ◽

Einstein Gravity ◽

Kinetic Term ◽

Cauchy Horizon ◽

Charged Scalar ◽

Inner Horizon ◽

Scalar Hair ◽

Scalar Potentials

Abstract We establish a no inner-horizon theorem for black holes with charged scalar hairs. Considering a general gravitational theory with a charged scalar field, we prove that there exists no inner Cauchy horizon for both spherical and planar black holes with non-trivial scalar hair. The hairy black holes approach to a spacelike singularity at late interior time. This result is independent of the form of scalar potentials as well as the asymptotic boundary of spacetimes. We prove that the geometry near the singularity takes a universal Kasner form when the kinetic term of the scalar hair dominates, while novel behaviors different from the Kasner form are uncovered when the scalar potential become important to the background. For the hyperbolic horizon case, we show that hairy black hole can only has at most one inner horizon, and a concrete example with an inner horizon is presented. All these features are also valid for the Einstein gravity coupled with neutral scalars.

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Use of the Magnetostatic Analogue In Electromagnetic Lens Engineering

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100068795 ◽

1970 ◽

Vol 28 ◽

pp. 360-361

Author(s):

John W. Coleman

Keyword(s):

Boundary Conditions ◽

High Performance ◽

Force Fields ◽

Optical Design ◽

Direct Conversion ◽

Design Engineering ◽

Design Data ◽

Scalar Potentials ◽

Geometric Elements ◽

At Will

In the design engineering of high performance electromagnetic lenses, the direct conversion of electron optical design data into drawings for reliable hardware is oftentimes difficult, especially in terms of how to mount parts to each other, how to tolerance dimensions, and how to specify finishes. An answer to this is in the use of magnetostatic analytics, corresponding to boundary conditions for the optical design. With such models, the magnetostatic force on a test pole along the axis may be examined, and in this way one may obtain priority listings for holding dimensions, relieving stresses, etc..The development of magnetostatic models most easily proceeds from the derivation of scalar potentials of separate geometric elements. These potentials can then be conbined at will because of the superposition characteristic of conservative force fields.

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