Static, spherically symmetric solutions of Yang-Mills-Dilaton theory

Static, spherically symmetric solutions of the Yang-Mills-Dilaton theory are studied. It is shown that these solutions fall into three different classes. The generic solutions are singular. Besides there is a discrete set of globally regular solutions further distinguished by the number of nodes of their Yang-Mills potential. The third class consists of oscillating solutions playing the role of limits of regular solutions, when the number of nodes tends to infinity. We show that all three sets of solutions are non-empty. Furthermore we give asymptotic formulae for the parameters of regular solutions and confront them with numerical results

Solitons of the Einstein-Yang-Mills Theory

Subject of this talk is an overview of results on self-gravitating solitons of the classical Yang-Mills-Higgs theory. One finds essentially two classes of solitons, one of them corresponding to the magnetic monopoles the other one to the sphalerons of flat space. The coupling to the gravitational field leads to new features absent in flat space. These are the gravitational instability of these solitons at the Planck scale and the existence of black holes with `non-abelian hair'' in addition to the regular solutions.Comment: 13 pages latex + 10 figure

On Nonlinear σ\sigma-Models arizing in (Super-)Gravity

In a previous paper with Gibbons [CMP 120 (1987) 295] we derived a list of three dimensional symmetric space $\sigma$-model obtained by dimensional reduction of a class of four dimensional gravity theories with abelian gauge fields and scalars. Here we give a detailed analysis of their group theoretical structure leading to an abstract parametrization in terms of `triangular' group elements. This allows for a uniform treatment of all these models. As an interesting application we give a simple derivation of a `Quadratic Mass Formula' for strictly stationary black holes.Comment: 33 pages, 1 tabl

Static Cosmological Solutions of the Einstein-Yang-Mills-Higgs Equations

Numerical evidence is presented for the existence of a new family of static, globally regular `cosmological' solutions of the spherically symmetric Einstein-Yang-Mills-Higgs equations. These solutions are characterized by two natural numbers ($m\geq 1$, $n\geq 0$), the number of nodes of the Yang-Mills and Higgs field respectively. The corresponding spacetimes are static with spatially compact sections with 3-sphere topology.Comment: 7 pages, 5 figures, LaTe

Classification of Static, Spherically Symmetric Solutions of the Einstein-Yang-Mills Theory with Positive Cosmological Constant

We give a complete classification of all static, spherically symmetric solutions of the SU(2) Einstein-Yang-Mills theory with a positive cosmological constant. Our classification proceeds in two steps. We first extend solutions of the radial field equations to their maximal interval of existence. In a second step we determine the Carter-Penrose diagrams of all 4-dimensional space-times constructible from such radial pieces. Based on numerical studies we sketch a complete phase space picture of all solutions with a regular origin.Comment: 49 pages, 19 figures, submitted to Commun. Math. Phy

Non-Abelian black holes: The inside story

Recent progress in understanding of the internal structure of non-Abelian black holes is discussed. Talk given at the international Workshop on The Internal Structure of Black Holes and Spacetime Singularities, Haifa, Israel, June 29 -- July 3, 1997.Comment: 23 pages, latex, contains 12 eps files combined in 8 figure

Non-Universality of Critical Behaviour in Spherically Symmetric Gravitational Collapse

The aim of the present letter is to explain the `critical behaviour' observed in numerical studies of spherically symmetric gravitational collaps of a perfect fluid. A simple expression results for the critical index $\gamma$ of the black hole mass considered as an order parameter. $\gamma$ turns out to vary strongly with the parameter $k$ of the assumed equation of state $p=k\rho$.Comment: 6

Pengaruh Lingkungan Belajar dan Minat Belajar Terhadap Hasil Belajar Matematika Siswa Kelas VII Semester Genap SMPN 3 Tungkal Ulu di Masa Pandemi COVID-19

Penelitian ini bertujuan untuk mengetahui pengaruh lingkungan belajar dan minat belajar terhadap hasil belajar matematika peserta didik di masa pandemic COVID-19. Metode penelitian yang digunakan adalah penelitian kuantitatif non eksperimen dengan ex-post-facto. Teknik pengumpulan data pada penelitian ini adalah tes dan angket. Analisis data dilakukan dengan uji prasyarat terdiri dari uji normalitas, linieritas, dan indepen. Selanjutnya dilakukan uji hipotesis dengan analisis regresi ganda. Berdasarkan hasil analisis diperoleh terdapat pengaruh yang positif dan signifikan antara lingkungan belajar di rumah dan minat belajar dengan hasil belajar matematika siswa kelas VII SMP Negeri 3 Tungkal Ulu Semester Genap Tahun Ajaran 2020/2021. Hal ini ditunjukkan dengan uji – F yaitu 6,593277831> 3,35. Koefisien korelasi ganda (R) sebesar 0,5728293921 dan koefisien determinasi (R2) sebesar 0,3281335125 dengan persamaan garis linear -38,333043313+0,4186176102 + 0,9070199850 X2 . Besar sumbangan relatif X1 sebesar 35,9591 % dan X2 sebesar 64,0409% serta sumbangan efektif X1  sebesar 11,7994 % dan X2 sebesar 21,01395%