How to change app default theme to a different app theme?

Actually you should define your styles in res/values/styles.xml. I guess now you've got the following configuration:

<style name="AppBaseTheme" parent="android:Theme.Holo.Light"/>
<style name="AppTheme" parent="AppBaseTheme"/>

so if you want to use Theme.Black then change AppBaseTheme parent to android:Theme.Black or you could change app style directly in manifest file like this - android:theme="@android:style/Theme.Black". You must be lacking android namespace before style tag.

You can read more about styles and themes here.

To change your application to a different built-in theme, just add this line under application tag in your app's manifest.xml file.

Example:

<application 
    android:theme="@android:style/Theme.Holo"/>

<application 
    android:theme="@android:style/Theme.Holo.Light"/>

<application 
    android:theme="@android:style/Theme.Black"/>

<application 
    android:theme="@android:style/Theme.DeviceDefault"/>

If you set style to DeviceDefault it will require min SDK version 14, but if you won't add a style, it will set to the device default anyway.

<uses-sdk
    android:minSdkVersion="14"/>

If you are trying to reference an android style, you need to put "android:" in there

android:theme="@android:style/Theme.Black"

If that doesn't solve it, you may need to edit your question with the full manifest file, so we can see more details